SOLUTION: A theater has 500 balcony seats and 1800 main level seats. If tickets for balcony seats will cost $15 less than tickets for main level seats, what should the prices be for each typ

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Question 952779: A theater has 500 balcony seats and 1800 main level seats. If tickets for balcony seats will cost $15 less than tickets for main level seats, what should the prices be for each type of ticket so that total revenue from a sellout performance will be $33,840?
Found 2 solutions by MathLover1, macston:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
A theater has 500 balcony seats and 1800 main level seats.

if all tickets sold:
500x and 1800y, the revenue R will be:
R=500x%2B1800y
If tickets for balcony seats x will cost $15 less than tickets for main level seats y, then
x=y-15
R=500%28y-15%29%2B1800y
what should the prices be for each type of ticket so that total revenue R from a sellout performance will be $33840:
$ 33840=500%28y-15%29%2B1800y......solve for y
$ 33840=500y-7500%2B1800y
$ 33840%2B7500=2300y
$ 41340=2300y
$ y=41340%2F2300
$ y=17.97391304347826
$ highlight%28y=17.974%29->price be for ticket for main level seats
then, x=y-15 will be
$x=17.974-15
$highlight%28x=2.974%29->->price be for ticket for balcony seats

check the revenue:
$R=500x%2B1800y
$R=500%2A2.974%2B1800%2A17.974
$R=1487%2B32353.2
$R=33840.2..round it
$R=33840


Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
B=balcony seats=M-$15; M=main level seats
500B+1800M=$33840 Substitute for B.
500(M-$15)+1800M=$33840
500M-$7500+1800M=$33840 Add $7500 to each side.
2300M=$41340
M=$17.97 ANSWER 1: Mail level seats cost $17.97
B=$17.97-$15=$2.97 ANSWER 2: Balcony seats cost $2.97
CHECK:
500($2.97)+1800($17.97)=$33840
$1485+$32346=$33840
$33831=$33840 (Difference due to rounding down 0.4 of a cent per ticket)